Pattern of Numbers

$786, 514, 378, 310, 276, ?$

Find first $20$ terms of the sequence:

$7,12, 17, .....$

If $a=b^2-b$, where $b$ is an integer then $a^2-2a$ is divisible by 

The largest common term to the sequences $1, 11, 21, 31, ....100$ terms and $31, 36, 41, 45, 46....100$ terms is

Identify the missing number $49,343,64,\dots ,81,729$

If $1^2 + 2^2 + 3^2 + ...... + {10}^2 = 385$, then the value of $2^2 + 4^2 + 6^2 + ..... + {20}^2$ will be _____.
 

$4, 13, 34, 73,$ _____

$6, 13, 32, 69,$ _____

$7, 16, 36, 74,$ _____

$5, 13, 23, 35,$ _____

$3, 7, 13, 21,$ _____

The $5^{th}$ terms of the sequence defined by $t_1=2$, $t_2=3$, and $t_n=t_{n-1}+t_{n-2}$ for $n\ge 3$.

In the given sequence find the value of $n$.

$6, 30, 150, n, 1350$

Next term in the sequence $21, 30, 39, 48, 57, ?$ is $65$

Fourth term in the sequence $4, 12, 36, ?, 324, 972$ is $109$

What is a sequence?

$2, 3, 13, 4, 5, 41, 6, 7, ?, ?$

$7+10+13+16+\dots$ is a sequence whereas $7,$ $10,$ $13,$ $16$ is a series.

If the sign $-$ and $+$ and the numbers $4$ and $8$ interchange their positions, then the value of $4-8+12=6$.

If the sign $÷$ and $+$ and the numbers $6$ and $3$ interchange their positions, then the value of $3+6÷5=7$.